A versatile method to fingerprint and compare the oxidative behaviour of lipids beyond their oxidative stability

In this work we propose the use of isothermal thermogravimetry to evaluate the oxidative stability of a lipid and to evaluate how the glyceride composition affects the entire oxidative process, to quantify the oxidation undertaken by the lipid, and numerically compare the oxidative behaviour of different lipids. The innovative aspect of the present method lies in the acquisition of a prolonged “oxygen uptake” curve (4000–10,000 min) of a lipid under oxygen and in the development of a semi-empirical fitting equation for the experimental data. This provides the induction period (oxidative stability), and allows to evaluate the rate of oxidation, the rate and the magnitude of oxidative degradation, the overall mass loss and the mass of oxygen taken by the lipid upon time. The proposed approach is used to characterize the oxidation of different edible oils with different degrees of unsaturation (linseed oil, sunflower oil, and olive oil) as well as chemically simpler compounds used in the literature to model the autoxidation of vegetable oils and lipids in general: triglycerides (glyceryl trilinolenate, glyceryl trilinoleate and glyceryl trioleate) and methyl esters (methyl linoleate and methyl linolenate). The approach proves very robust and very sensitive to changes in the sample composition.

www.nature.com/scientificreports/ mass loss region carried out with a single exponential is not sufficiently accurate. The term t 0 in the sigmoidal function, accounts for the delay observed in the mass increase and, therefore, correlates with the induction time in the peroxide formation process. The value of the time constant 0 is correlated with the rate of the oxygen uptake. The time constant 1 , and when used 2 , are correlated with the rate of all phenomena leading to mass loss, q and ( 1 − q) being the relative weight of the two exponentials, when both present. The choice of using exponential functions to describe both the oxygen uptake step and the loss of mass implicitly implies that the underlying kinetic processes are assumed to be of the first order or the pseudo first order with respect to the substrate concentration. This assumption is in accordance with what is reported in the literature for these experiments when carried out under non-limiting oxygen conditions 53,54 . An analysis of experimental curves shown in previous works 31,32 suggests that it should always be 0 ≫ 1 , 2 , since the derivative dmass% dt , evaluated at the two inflection points, is always significantly greater, in absolute value, during mass gain versus mass loss. In these works 31,32 we proposed the use of fitting functions of the type: or Since all exponentials cancel out when t approaches infinity, B represents the value of the function at the plateau. When t tends to zero, the function tends to A 1+e 0 t 0 + B , therefore the mass% at time zero should be between A 2 + B(when 0 t 0 tends to zero) and B (when 0 t 0 is large). Therefore, the two previously proposed functions can describe accurately oxygen uptake curves when the induction times are relatively short, with a small inaccuracy only in the initial part, easily disguised by the experimental error. In cases where t 0 (and consequently 0 t 0 ) is large, the functions 1a and 1b tend instead to the constant value B both at the limit for t → ∞ and for t → 0 , which makes the fitting clearly unacceptable in all those cases in which the experimental trend shows a step between the initial plateau and the asymptotic value for t → ∞.
We therefore here propose the new following functions: or to accurately interpolate oxygen uptake curves independently from the value of t 0 . The functions (2a) and (2b) tend asymptotically to the value 100 − B when t → ∞ , while for t → 0 they acquire values in between A−B 2 + 100 and 100 . From the point of view of the interpretation of the fitting kinetic parameters, i.e. the time t 0 and the time constants 0 , 1 and 2 , nothing changes with respect to the fitting Eqs. (1a) and (1b). The same can be said about the meaning of the parameter q, which quantifies the relative weight of the two decreasing exponentials, when both are present. The meaning of A and B in Eqs. (2a) and (2b), however, is different. To summarize, the meaning of each parameter of the new equations, Eqs. (2a) and (2b), is as follows: • A: amplitude factor of the exponential function (or of the exponential functions) associated with the loss of mass. • B: deviation of the curve from 100% as t tends to infinity. • λ 0 : apparent rate constant related to the mass increase.
• λ 1 and λ 2 : apparent rate constants associated to the mass loss.
• q and (1 − q) (0 ≤ q ≤ 1): relative weights of the two relevant processes responsible for the mass loss.
• t 0 : is the abscissa of the inflection point of the sigmoidal function, related to the induction time of the oxygen uptake.
To estimate the amount of mass of oxygen added, and the total mass loss due to oxidative degradation, we here introduce two more parameters, A corr = Ae − 1 t (or A corr = A qe − 1 t + 1 − q e − 2 t ) calculated at the t onset and C = A corr − B . t onset is the abscissa of the intersection point between the baseline and the tangent to the curve at the first inflection point. The meaning of parameters B and C and A corr is exemplified in Fig. 1.
Oxygen uptake profiles and data fitting. An oxygen uptake profile was recorded for each sample by isothermal thermogravimetric analysis under air flow. The shape of the curve has been proven to be affected not only by the oil composition, but also by external parameters, including the temperature of analysis 18,19,23,24 . Several efforts have been devoted in the literature to find the working temperature that allows to carry out the isothermal experiments in a relatively short time, without significantly affecting the reaction pathways with respect to those occurring at ambient temperature 18,19,23,24 . A wide range of temperatures, from 80 to 150 °C, has been investigated. In the analysis of vegetable oils, 80-90 °C are considered the best compromise between a faster (1a) www.nature.com/scientificreports/ oil oxidation rate and a reliable oxygen uptake curve 20,22,31 . In our work, thermogravimetric curves of plant oils and triacylglycerols were recorded at 80 °C. During preliminary experiments on methyl linoleate, the first step of mass increase was not visible at 80 °C and only a sharp decrease of mass was observed. For this reason, methyl linoleate and methyl linolenate were analysed at 60, 55, 50 and 40 °C. Methyl oleate was analysed only at 40 °C since already under this relatively low temperature only a slow mass decrease was observed within 8000 min of analysis (Fig. 3b). Figure 2a shows the experimental thermogravimetric curves and the fitting curves calculated by Eq. (2a) for plant oils (linseed oil, Lo, sunflower oil, So, and olive oil, Oo). Table 1 displays the curve-fitting parameters and their standard error, along with the relative χ 2 and R 2 coefficients, which indicate the quality of the fittings. χ 2 and R 2 values for both linseed oil and sunflower oil are very good, but not as good for olive oil; for the latter the fitting equation is intrinsically unable to describe the experimental trend in the short interval between the end of mass increase and the beginning of mass loss, although it still perfectly describes the mass increase and the mass loss regions, and all the kinetics parameters show very small standard errors. Since in Oo the mass loss is delayed respect to the mass uptake, in this particular case, the parameter C (effective total oxygen taken by the sample) is the value of the maximum of the curve, while the total mass loss of the sample is the difference between the maximum and the end of the curve (A corr calculated at t endset that is the abscissa of the intersection point between the baseline before the mass uptake and the tangent at the inflection point of the mass decay). Figure 2b shows the experimental thermogravimetric curves and the fitting curves calculated according to Eq. (2b) for triacylglycerols, while Table 1 displays the curve-fitting parameters and their standard error, in brackets, along with the χ 2 and R 2 coefficients obtained. The similarity between the oxygen uptake curves of plant  www.nature.com/scientificreports/ oils and those obtained for pure triacylglycerols, is rather evident. OOO shows the same short delay between the mass increase and the mass loss as Oo and the fitting equation describes well the mass increase and the mass loss regions but is inadequate to fit the small interval in between. C and A corr for OOO are thus calculated as for Oo.

Oils, triglycerides, and methyl esters.
A corr and C parameter of the triacylglycerols are calculated in the same way as described above for the oils Table 1. Figure 3 shows the experimental and calculated curves for methyl linolenate and methyl linoleate, while the fitting parameters obtained at different temperatures are reported in Table 2. Although the general shape of the curves reflects quite well that of the corresponding triglycerides, it should be noted that the oxygen uptakes were measured at temperatures different than those of oils and acyl glycerides and therefore the fitting parameters must be compared with caution.
By comparing the fitting parameters of the investigated systems with different PUFA content we can easily compare their oxidative behaviour as discussed in detail in the following paragraphs.
Induction time. t 0 values reflect the trend of the oxidative stability of the lipid, and it has an inverse dependence on the number of unsaturations 41 . However, in plant oils, antioxidants play a major role in inhibiting or retarding the autoxidation process 55 . It is thus not straightforward to distinguish, in the oils, the contribution, or the extent of the effect of the antioxidants and the oxidative stability of the constituting glycerides. The oxidative stability because of the number and type of unsaturations is clearly visible when we compare the t 0 values of acylglycerols which do not contain antioxidant.
Mass uptake. Comparing the fitting parameters C and λ 0 related to the mass uptake, the observed trend is that linseed oil/glyceryl trilinolenate/methyl linolenate take more oxygen than sunflower oil/glyceryl trilinoleate/ methyl linoleate which, in turn, take more oxygen than olive oil/trioleine (see Tables 1 and 2). The rate of autoxidation varies in the same order except for triglycerides for which λ 0 is slightly higher for glyceryl trilinoleate than glyceryl trilinolenate, although λ 0 of glyceryl trioleate is still the lowest. The trends of the parameter C is perfectly consistent with the number of double bonds present in the different materials, as the concentration of the primary oxidation products (hydroperoxides) as well as the maximum autoxidation rate increase with the concentration of unsaturations 56,57 . It also relates with the MBI index, that is the number of bis-allylic positions, as these are more susceptible to oxidation with respect to the allylic positions 37,41,58 . Linolenic, linoleic, and oleic acids present, respectively, two bis-allylic positions at C-11 and C-14, one bis-allylic position at C-11, and none. When we consider the numerical values, small differences are observed between the oils and the corresponding acylglycerols, which can be easily explained by considering the differences in their chemical composition, supporting the robustness of the fitting model. On the other hand, methyl esters are much faster to react and take up more oxygen. This different behaviour can be ascribed to the different mobility of the unsaturated tails in the two systems and to the higher viscosity of triglycerides compared to that of methyl esters which slow down the oxygen diffusion. These factors can both affect speed and pathways of reactions.
Mass loss. Oils with the greatest PUFA content produce the lowest amounts of secondary oxidation products, which comprise volatile species 59 . This is not only related to the number of unsaturations in general, but, again, to the number of bis-allylic positions available upon oxidation. Peroxyl radicals can abstract hydrogens only in bis-allylic positions, while alkoxyl radical may also abstract hydrogens in allylic positions 60 . As a result, the www.nature.com/scientificreports/ concentration of bis-allylic positions affects the reaction pathways: a high concentration of bis-allylic hydrogens favour propagation through radical abstraction, while addition of peroxides to double bonds is favoured in lipids with few bis-allylic hydrogens available 60 . The final result is that a high number of bis-allylic position favours cross-linking, while lipids with a low or null content of bis-allylic positions are more prone to oxidative degradation 6 . The fitting parameter A (amplitude of the decreasing exponential) is in line with this observation, showing that linseed oil/glyceryl trilinolenate/methyl linolenate is less prone to oxidative degradation with respect sunflower oil/glyceryl trilinoleate/methyl linoleate and olive oil/triolein, and that lipids based on oleic acid show the highest oxidative degradation. As in polyunsaturated systems, in monounsaturated ones, peroxides and other oxidation intermediates are formed and they break down to a wide range of secondary oxidation products which include volatiles compounds 61 . Differently from oleic acid based oils and triglycerides, the experimental mass change of methyl oleate shows only a slow mass loss (Fig. 3b). Since this compound is not subject to crosslinking to a significant extent, it is possible to speculate that the evolution of volatile compounds occurs on the same timescale of the primary oxidation giving rise to a globally decreasing trend of the mass percent.
Methyl linoleate and methyl linolenate at different temperatures. The shape of oxygen uptake curves does not only and unilaterally relate to the composition of the fatty acid substrates but also to reaction conditions and in particular to the temperature of analysis, which necessarily influences the reaction pathways 18,19,23,24 . As methyl esters are more reactive than triglycerides 9 , they were selected to investigate the effect of temperature on the oxidative behaviour of polyunsaturated lipids, by carrying out isothermal thermogravimetry at different temperatures (40, 50, 55 and 60 °C). Figure 4 shows the experimental and fitting curves [obtained from the fitting Eq. (2a)] for methyl linoleate and methyl linolenate at 40, 50, 55 °C along with those at 60 °C, already discussed, for comparison. The fitting parameters are displayed in Table 2.
The higher the temperature of analysis, the lower the maximum reached by the mass %. This can be related to the rate of decomposition of hydroperoxides. Richaud et al. 28 carried out a study on the oxidation of methyl esters of oleic, linoleic, and linolenic acids based on chemiluminescence intensity data over time. The authors observed that the maximum of the curves of chemiluminescence intensity increases with temperature. The chemiluminescence signal is mainly related to the rate of hydroperoxides bimolecular decomposition: the higher the temperature, the higher the decomposition rate. The increase of hydroperoxides decomposition observed at higher temperatures promotes oxidative degradation, resulting in a lower mass % at the maximum of the curves.
Curves obtained at the different temperatures (40, 50, 55, and 60 °C) can be fitted with Eq. (2a). The fitting of experimental data at 40 °C is quite unsatisfactory, though. This is because the experimental measurement was stopped when the descent had not yet assumed a decreasing exponential trend. For this reason parameters A, B and C are not reported in Table 2. Nevertheless, considerations on the mass increase among the four temperatures (40, 50, 55 and 60 °C) are still possible. The higher the temperature of analysis, the smaller are the values of t 0 and t onset and the higher are the values of the rate constant λ 0 . This is in agreement with previous work that showed that, when increasing the temperature of analysis, the induction time becomes smaller 25 , while the rate of hydroperoxides formation increases 29 . When the temperature rises (see parameters obtained at 50, 55 and 60 °C- Table 2), the parameters that estimate the total loss of mass and the amount of oxygen taken up, An Arrhenius plot can be built using the values of λ 0 at different temperatures, to estimate the apparent activation energy of the oxygen uptake process. The logarithm of λ 0 decreases linearly with the reciprocal of temperature for both methyl esters (R 2 = 0.9197 and 0.9759 for methyl linoleate and methyl linolenate, respectively). The activation energy (E a = -slope⋅R) of the uptake of oxygen was evaluated: E act (methyl linoleate) = 55.6 ± 11.6 and E act (methyl linolenate) = 44.2 ± 4.9 kJ mol −1 . Methyl linolenate has an activation energy for the uptake of oxygen lower than methyl linoleate. The values are consistent with literature data obtained by chemiluminescence intensity data 28 and gas-chromatography 62 and data from non-isothermal DSC curves for ethyl linolenate and ethyl linoleate 37,63 .
Comparing the A, A corr and C parameters obtained at 50, 55 and 60 °C, it is quite clear that the higher the temperature of analysis, the lower the amount of mass increase because of oxygen addition, and the higher the mass loss. The higher mass loss observed at higher temperatures could have several possible explanations. At higher analysis temperatures the rate of evaporation of the compounds produced by oxidation will be greater. Moreover, at higher temperatures, one can expect a higher mobility of molecules in the sample, which could affect reaction pathways. Finally increasing temperatures of analysis might overcome activation barriers which are in place at low temperature.
Glyceryl trilinoleate and glyceryl trilinolenate at 25 °C. Based on the experiments carried out at different temperatures on methyl esters (paragraph 3.4), it is expected that kinetic parameters, and extent and rate of reaction with oxygen are different upon natural rather than accelerated analysis conditions. To visualize the extent of this difference, the experimental oxygen uptake profiles of glyceryl trilinoleate and glyceryl trilinolenate at 25 °C were recorded by weighing the same sample with a microbalance over a period of two months. The curves are shown in Fig. 5. The observed trends are qualitatively very similar to those recorded at 80 °C by TG. The experimental data obtained at 25 °C in natural ageing conditions were fitted with Eq. (2a) although in this case, given the small number of experimental points (about 10 points for each system), the statistical significance of the fitting parameters is less good than those obtained with the TG experiments. The curve-fitting parameters obtained are reported in Table 3. The most evident difference, obviously excluding the different time scale, is that, at room temperature, the mass increase % is higher than that at higher temperature, as already observed for methyl esters and reported in literatures for plant oils 23 . Another difference concerns the apparent rate constants related to the mass increase (λ 0 ) . At 80 °C λ 0 values are very similar for both triacylglycerols (2.5 × 10 -2 and 2.8 × 10 -2 for glyceryl trilinolenate and glyceryl trilinoleate, respectively), whereas at 25 °C, λ 0 of glyceryl trilinolenate is twice than that of glyceryl trilinoleate (10 -3 against 5 × 10 -4 ).
Comparison of the two model equations. As a further test, the new model equations were tested on polyunsaturated oils (linseed and safflower oil) already studied in our previous work 31 . TG curves of linseed and safflower oil, recorded under isothermal conditions at 80 °C were fitted according to the old Eq. (1b) and the new Eq. (2b). Table 4 reports the results of both fitting procedures. The numerical values obtained are generally perfectly consistent with each other, highlighting the same trends, thus leading to the same conclusions. www.nature.com/scientificreports/

Conclusions
The present work proposes semi-empirical fitting equations for the prolonged oxygen uptake curve of a lipid obtained by isothermal thermogravimetry. The aim is to obtain numerical parameters that describe the crucial steps of the oxidation process: the induction period, the rate of oxidation due to the formation of peroxides, an estimate of the amount of oxygen which reacts with the sample, and the rate and magnitude of oxidative degradation. The fitting method is sensitive to the chemical differences between the samples, providing numerical parameters which can be related to the reactivity of different classes of lipids, characterized by different PUFA content and the MBI values, with oxygen.
The values that describe the rate and extent of reaction with oxygen depend strongly on the temperature of analysis. Data show that working in accelerated conditions at higher temperature, provides, in reasonable times   www.nature.com/scientificreports/ of analysis, a quite good description of the oxidative behavior of a lipid. In general, though, the higher the temperature of analysis, the more oxidative degradation is observed. Above all, the method allows to obtain reliable comparisons among the oxidative behavior of different samples. The equation model was thus used to describe and compare oxygen uptake curves of linseed oil (rich in linolenic acid), sunflower oil (rich in linoleic acid) and olive oil (rich in oleic acid), as well as triacylglycerols (glyceryl trilinolenate, glyceryl trilinoleate and glyceryl trioleate) and methyl esters (methyl linolenate, methyl linoleate, methyl oleate). The comparison between the curves obtained shows that triacylglycerols are very good models to describe the oxidative behavior of oils, excluding the influence of natural antioxidants present in an oil, which may vary considerably. Methyl esters, on the other hand, are more reactive than the corresponding triglycerides. So, although they are less suited than acylglycerols to mimic the oxidative behavior of plaint oils, especially from the kinetics point of view, they are significantly cheaper and better suited to molecular studies on the degradation mechanisms by mass spectrometry. The study performed on the oxidative degradation of methyl esters becomes particularly relevant due to their use as biofuels. We can conclude that the model to study lipid behavior must be chosen carefully, and that the proposed fitting equations represents a useful tool to guide this choice and support data interpretation.

Data availability
The data generated and analysed during this study which are not already included in this published article are available from the corresponding authors on reasonable request.